limites merad 3 s m mt.pdf
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7/25/2019 limites merad 3 s m mt.pdf
1/4
x
f(x)
0
lim ( )x
f x lx
=
1
2016-2015
-33
1
..
3
5 10
13
l
0x
0k
=
0- 0+ :
k
0
k=
+- : k0
k + = - + :
k = - + :
k
1:f(x)+x+
:lim ( )x
f x+
=+
:
lim ( )x
f x+
=lim ( )x
f x
=+lim ( )x
f x
=
2:f(x)Lx+
:
lim ( )x
f x L+
=
L
y=L
lim ( )x
f x L
=
3: f(x)+xa :
lim ( )x a
f x
= +
lim ( ) ; lim ( )x a x a
f x f x +
= =
lim ( )x a
f x+
= +
x=a
a
y=ax+b
( )lim ( ) 0x
f bx ax
= +
0
; 0 ; ;0
y=ax+b
1
2
:
3
:
.
. .
.
1:
1( .
2( .
)(: () ax xf b g x+= +lim 0( )
xg x
= 4/1
1- 2-
)
( 3- 4- 5-
-
7/25/2019 limites merad 3 s m mt.pdf
2/4
.... ....
( )limx
g x l +
=( )limx
h x l +
=
( ) ( ) ( )g x f x h x
( )l imx
f x l +
=
( )limx
g x+
=
( ) ( )f x g x
( )limx
f x+
=
( ) ( )x g x
( )limx
g x+
= +
( )limx
f x+
= +
x :;
...
2:
2
; 0 ; 0 ,
; 0 ; 0 ,
x x
x x xx
x x x
+
=
+ =
0
0
3:
xa :
1( (:(x-a 2((x-a) . x=a)3
4:
:
:x :
:xa :
1( .2( :
)3 .x=a
( ) ( ) ( ); ;a b a b a b
0
0
( )( )( )( )
( )( )
2
2
a b a b a b
a b a b a b
a b a b a b
+ =
+ =
+ =
5:
: 1( sin:cos2( (
(
0 0 0
1 cos 1; 1 sin 1
sin sinlim lim lim 1
sinx x x
x x
x x ax
x x ax
+ +
= = =
( ) ( )lim ( )x a
f x f af a
x a
=
6:l'Hospital
0;0
..
..
..
4/2
-
7/25/2019 limites merad 3 s m mt.pdf
3/4
1 cos( )
xg x
x
+=
+-
.
+:
1. x>0,x)
2+1(
-
7/25/2019 limites merad 3 s m mt.pdf
4/4
lim ( )x
f x
=
( )lim
x
f x
x
0
+
0a
+
[ ]lim ( )x
f x ax
b
y ax=
y ax b= +
) (
2
21
11) lim
3 2x
x x
x x
+ +
+0
1 2 12)lim
x
x x
x
+ +
2 1 23) lim
3xx x
x + + +
+0
1 2 14)lim1 4 1 3x
x xx x
+ + +
15) lim
2x
x x
x x+
+
+
2
1
1 16)lim
1x
x x
x
+
f )Cf(
:
:1. f . 2. . 3. )Cf.(
4.
)Cf(
.
{ }1R
8
f )Cf(
:
1. y=2
)Cf.(2.f(x)=0 .3. f(x)>0
4.
x< -25.
{ }1R
{ }1R
] [; 1
f(-2)>f(x)
( )3;1A )Cf.(
9
2
2 4
0 1
6 5 37) lim 8) lim
2 2 4
2 19) lim 10) lim
11 1
x x
x x
x x x
x x x
x x x
xx
+ +
+ 2 2
2 2
2
4 1 2 111) lim 12) lim
4 1 4
13) lim 14) lim 1
x x
x x
x x x x x
x x x x x
x x x x
+
+ +
+ + + +
+ +
+ +
:
:
:
4/4
